Logic 4.4

“No cats are dogs” = “No dogs are cats”
“Some dogs are black” ≠ “Some dogs are not black”

Conversion, Obversion, and Contraposition yield new propositions that may or may not have the same truth-value depending on the starting proposition.

Conversion: Switching the subject and predicate terms. E and I propositions are Logically Equivalent, while A and O propositions are not.

Conversion for E and I propositions can be used to make immediate inferences. A and O propositions cannot, and are therefore Illicit Conversions.
Ex:
“All cats are dogs. Therefore, all dogs are cats”
“Some animals are not dogs. Therefore, some dogs are not animals.” Both of the these arguments commit the fallacy of illicit conversion.

Obversion: 1) Change the quality; 2) replace the predicate with its term opposite.
Ex: All S is P
Step 1: No S is P; Step 2: No S is non-P
“All cats are animals” becomes “No cats are non-animals.”

The class complement is the opposite of class term.

When an obversion is made then made again, the proposition will be the same as the starting proposition:
“All presidents of the United States are citizens”
Obversion:
“No presidents of the United States are non-citizens”
Obversion:
All presidents of the United States are citizens”

All obversions retain their truth-value.

Ingenuity is required to find a term’s complement. All immediate inferences from obversion are valid.


Contraposition: 1) switch the subject and predicate terms; 2) Replace the subject and predicate terms with their complement.

All S is P—All non-P is non-S

A and O propositions retain their truth-value in contraposition, while E and I propositions do not.

Inferences from E and I props are logically licit, while inferences from A and O propositions are logically illicit.

In order to remember which propositions retain their truth value for conversion and contraposition remember the second and third vowels of each word:

ConvErsIon
ContrApOsition